Earth orientation

Earth orientation Earth orientation is defined as the instantaneous angular relationship between an Earth-fixed reference frame and an inertial, external reference frame. Intimately linked with this concept is that of Earth rotation or rate of change of orientation over timescales of from thousands of years to a few hours. To first approximation, the Earth in its annual orbit about the Sun is inclined such that the angle, the obliquity, between the Earth's equator and the orbital plane, the ecliptic, is approximately 23.4 degrees, and the Earth's rotational axis is fixed in inertial space. The Earth spins about this axis in a period of 24 hours, or 86400 seconds. The study and observation of Earth orientation and the development of a theoretical understanding of the processes affecting Earth rotation seek to improve the parameters of this model so that orientation at any instant may be determined at the centimetre level of accuracy.

The Earth is an oblate spheroid, with polar diameter some 45 km less than the equatorial diameter. The gravitational attraction of the Sun and Moon on the resultant equatorial bulge causes the rotational axis to precess smoothly about the pole of the ecliptic with a period of some 25600 years. Superimposed on this smooth precession is a somewhat irregular small-amplitude motion (nutation) at periods of from a few days to 18.6 years, due to the gravitational attractions both of the Sun and of the Moon during its complex orbit about the centre of gravity of the Earth–Moon system. The ecliptic itself moves slowly in inertial space, owing to the gravitational attraction of the planets on the Earth, such that the obliquity changes very slowly with time.

In addition to the precession and nutation of the Earth's rotational axis, the Earth itself undergoes a wobble such that the crust wanders about the rotational axis with a combination of two periods and amplitudes. One motion, called the Chandler wobble, occurs at the natural resonant frequency of the Earth and its oceans, having a period of about 435 days and amplitude on the surface of the Earth of about 6 m. The second, annual, wobble is understood to be atmospherically excited and has amplitude about 3 m. Together these wobbles are referred to as polar motion.

The rotational period of the Earth (or length-of-day, LOD) is not constant, varying from the standard 86 400 seconds by several milliseconds over a range of periods, as outlined here.

The tidal interaction between the Moon and the Earth is such that the Moon in its orbit exerts a retarding torque on the spinning Earth and slows its rotation thus causing a linear increase in LOD, of about 2 milliseconds per century. To conserve angular momentum within the Earth–Moon system, the Moon responds by increasing its orbital distance from the Earth at a rate of some 3 cm each year. In addition, the tides raised both in the oceans and in the solid Earth by the Moon and Sun cause changes in angular momentum of the Earth, with resultant short-periodic changes in LOD of up to one millisecond. Interactions between the Earth's core and solid mantle are believed to be responsible for changes in LOD of several milliseconds, over periods measured in decades. Exchanges of angular momentum between the atmosphere and the rugged surface of the Earth on annual timescales can cause periodic changes in LOD of up to one or two milliseconds in a matter of a few weeks.

As a result of these mechanisms, on average over recent years the LOD has been about 2 milliseconds longer than the standard day as kept by uniform atomic clocks, the basis for the worldwide timescale, UTC. This excess accumulates day by day, so that after about 18 months the timescale as determined by monitoring the rotation of the Earth, which is referred to as UT1, loses about one second as compared with UTC. By international agreement, one-second leap seconds are periodically introduced into UTC, in this case to delay its progress and keep civil timekeeping in step with the rotation of the Earth.

Earth orientation is monitored on a routine basis by worldwide networks of observational facilities and analysis centres. There are two classes of technique, astronomical and space geodetic. They contribute complementary and necessary duplicate information leading to very accurate, rapid determination of all the components of Earth orientation for a variety of operational and research activities.

A network of radio telescopes makes interferometric observations of compact extra-galactic radio sources whose positions define an inertial system with respect to which precession, nutation, polar motion and the difference between atomic time and UT1 are determined.

A network of optical telescopes makes laser range measurements with centimetric accuracy to Earth-orbiting satellites and in a few cases to the Moon. The observations are analyzed to determine both the orbital motions of the satellites and the Earth orientation parameters polar motion and LOD. Similar analyses of the navigational signals from the satellites of the US Global Positioning System are also used routinely to determine components of Earth orientation.

Figure 1 shows a series of LOD values for five years, determined from satellite laser range measurements and expressed as excess LOD in milliseconds with respect to the standard day of 86400 seconds. For clarity in the presentation, the predictable, short-period variations in LOD caused by the tidal interaction of the Moon have been removed from the data. Clearly seen are the annual, atmospherically driven variations in LOD, of amplitude between one and two milliseconds. Also apparent is the trend towards smaller values of excess LOD. If this trend continues, the introduction of leap seconds into UTC will become less frequent.

Graham M. Appleby

Bibliography

McCarthy, D. (ed.) (1996) International Earth Rotation Service Technical Note 21: IERS Conventions. Observatoire de Paris, 61 Avenue de l'Observatoire, Paris.
Munk, W. H. and and Macdonald, G. J. F. (1960) The rotation of the Earth. Cambridge University Press, New York.